The Russell 2000, the CAPM, and why is it so hard to stay market neutral

Samsara (the fund I run) uses primarily Russell 2000 futures to hedge. Through most of the history of the fund we have been net market long, but in the middle of 2010 I made a fateful decision to try to be close to market neutral. After a while of experiencing something unpleasantly like spitting in the wind, I started wondering whether I was using the right hedging instrument. Indeed, consider the following graph of recent performance of IWM (the Russell 2000 ETF) versus that of SPY (the S&P 500 ETF) [I use the ETF instead of the underlying index because the ETFs take account of the dividends paid by the index constitutents -- the expense ratio of the two ETFs is close to the same, so does not affect the comparison):

You will see that while both indices did well, the IWM outperformed the SPY by some seven percent over the (roughly) six months.

Since both indices were up (a lot), a natural hypothesis is that CAPM (the capital assets pricing model) should explain the difference: The Russell is viewed as riskier, so has a beta greater than one versus the more staid S&P 500. To test this, I did the following experiment: I compared IWM and SPY from the inception of IWM (5/30/2000), and ran a regression of IWM vs SPY log returns going back sixty trading days (so roughly a calendar quarter). 

Here is what we get: First, we see that the beta is highly variable, as seen in the table below:

As is the alpha:

But it also is clear that alpha is bouncing around close to zero (the huge spikes up and down in the fall of 2008 should not surprise those of us who lived through the period). In fact, the average alpha is the not-so-high 0.4 basis points per day (which means that if you kept rebalancing your portfolio of long IWM and short SPY to keep it 60-day-beta-neutral, you would make a princely 1% a year, not accounting for transaction costs (which would certainly eat up all of your profit).

So, a victory for the CAPM! Or is it? Look at the graph of betas again. You will see that in times of bull markets beta increases, while in times of crisis we see the much-discussed "phase-locking" behavior: betas converge back to 1. Indeed, if you were to hold a dollar neutral portfolio (long IWM, short SPY) for the eleven years of this study, you would have made 80 cents on your long dollar, with a Sharpe ratio of around 0.5, and max drawdown of around 20% (by contrast, simply being long IWM would have made you a little more money ($1.10) with a lot more volatility: the Sharpe Ratio would be close to 0.24, and the drawdown a stomach churning 60%. A picture is worth a thousand words:

The green curve is the return of SPY, which seems to have all of the downsides (huge drawdown) and none of the upside of the other two methods. Over the study period, the IWM runs a beta of fairly close to 1 vs SPY (1.09) , and alpha of around 2bp per day, or around 5% a year. (we could have gotten better Sharpe ratio by using the historical 1.09 beta to hedge our IWM holdings, but that could be viewed as cheating, while the beta of 1 is the reasonable bayesian prior.

What is the moral of the story? It seems that CAPM works in the short term, and if you want to hedge your long positions, Russell index futures are somewhat more cost effective than S&P 500 index futures (lower margin requirements). However, in the long term, it seems that small cap stocks outperform strongly in bull markets, and do not underperform much in bear markets, and so are a much better long-term investment.

Of course, your mileage can (and usually does) vary.